Some New Gronwall-Bellmann Type Discrete Fractional Inequalities Arising in the Theory of Discrete Fractional Calculus
نویسنده
چکیده
In this paper, we present some new GronwallBellmann type discrete fractional sum inequalities, and based on them present some Volterra-Fredholm type discrete inequalities. These inequalities are of new forms compared with the existing results in the literature, and can be used in the research of boundedness and continuous dependence on the initial value for solutions of fractional difference equations. As for applications, we apply the presented results to research the initial value problem of a certain fractional difference equation. MSC 2010: 26A33; 26D15
منابع مشابه
New classes of Lyapunov type inequalities of fractional $Delta$-difference Sturm-Liouville problems with applications
In this paper, we consider a new study about fractional $Delta$-difference equations. We consider two special classes of Sturm-Liouville problems equipped with fractional $Delta$-difference operators. In couple of steps, the Lyapunov type inequalities for both classes will be obtained. As application, some qualitative behaviour of mentioned fractional problems such as stability, ...
متن کاملSome New Discrete Fractional Inequalities and Their Applications in Fractional Difference Equations
In this paper, some new Gronwall-Bellman type discrete fractional difference inequalities and fractional sum inequalities are established. Based on the theory of discrete fractional calculus, explicit bounds for unknown functions concerned are presented. These inequalities can be used as a handy tool in the qualitative analysis of solutions of discrete fractional difference equations. As for ap...
متن کاملFractional difference inequalities of Gronwall – Bellman type
Discrete inequalities, in particular the discrete analogues of the Gronwall–Bellman inequality, have been extensively used in the analysis of finite difference equations. The aim of the present paper is to establish some fractional difference inequalities of Gronwall–Bellman type which provide explicit bounds for the solutions of fractional difference equations.
متن کاملSome new results using Hadamard fractional integral
Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse ...
متن کاملSome new variants of interval-valued Gronwall type inequalities on time scales
By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.
متن کامل